Chapter 1

Measurement

Realms of Physics • Physics provides a unified description of basic principles that govern

physical reality.

• Fundamental science: motion, force, matter, energy, space, time, …

• Convenient to divide physics into a number of related realms.

– Here we consider six distinct realms:

1.1 What is Physics? http://www.youtube.com/watch?v=qxXf7AJZ73A

1.2 Measuring things

• We measure each quantity by its own ―unit‖ or

by comparison with a standard.

• A unit is a measure of a quantity that scientists

around the world can refer to.

• This has to be both accessible and invariable.

Example:

1 meter (m) is a unit of length. Any other length can be

expressed in terms of 1 meter. A variable length, such

as the length of a person’s nose is not appropriate.

1.3 International System of Units (SI)

• The SI system, or the

International System of Units, is

also called the metric system.

• Three basic quantities are

length, time, and mass.

• Many units are derived from this

set, as in speed, which is

distance divided by time.

• Seven fundamental physical quantities & units:

– Length: the meter (m)

– Time: the second (s)

– Mass: the kilogram (kg)

– Electric current: the ampere (A)

– Temperature: the kelvin (K)

– Amount of a substance: the mole (mol)

– Luminous intensity: the candela (cd)

• Supplementary units describe angles:

– Plane angle: the radian

– Solid angle: the steradian

1.3 International System of Units

1.3 International System of Units

Scientific notation expresses results

with powers of 10.

Example:

3 560 000 000 m = 3.56 x 109m.

Sometimes special names are used

to describe very large or very small

quantities (as shown in Table 1-2).

Example:

2.35 x 10-9 = 2.35 nanoseconds (ns)

Powers of 10 Simulation:

http://micro.magnet.fsu.edu/primer

/java/scienceopticsu/powersof10/

• Based of the base units, we may need to change the units

of a given quantity using the chain-link conversion.

• Example: Since there are 60 seconds in one minute,

• Conversion between one system of units and another can

therefore be easily figured out as shown.

• The first equation above is often called the ―conversion

factor‖.

1.4 Changing units

ss

xx

ands

s

120)min1

60(min)2()1(min)2(min2

,min1

601

60

min1

• Units matter!

• Measures of physical quantities must always have the correct units.

• Conversion tables (Appendix C of the textbook) give relations between

physical quantities in different unit systems:

– Convert units by multiplying or dividing so that the units you don’t

want cancel, leaving only the units you do want.

– Example: Since 1 ft = 0.3048 m, a 5280-foot race (1 mile) is equal to

– Example: 1 kilowatt-hour (kWh, a unit of energy) is equivalent to 3.6

megajoules (MJ, another energy unit). Therefore a monthly electric

consumption of 343 kWh amounts to

0.3048 m

5280 ft 1609 m1 ft

33.6 MJ343 kWh 1.23 10 MJ 1.23 GJ

1 kWh

1.4 Changing units

Significant Figures

• The answer to the last example in the preceding slide is 1.23 GJ — not

1234.8 MJ or 1.2348 GJ as your calculator would show.

– That’s because the given quantity, 343 kWh, has only three significant

figures.

– That means we know that the actual value is closer to 343 kWh than to 342

kWh or 344 kWh.

– If we had been given 343.2 kWh, we would know that the value is closer to

343.2 kWh than to 343.1 kWh or 343.3 kWh.

• In that case, the number given has four significant figures.

– Significant figures tell how accurately we know the values of physical

quantities.

• Calculations can’t increase that accuracy, so it’s important to report the

results of calculations with the correct number of significant figures.

1.4 Changing units

Rules for Significant Figures

• In multiplication and division, the answer should have the same number of

significant figures as the least accurate of the quantities entering the calculation.

– Example: (3.1416 N)(2.1 m) = 6.6 N·m

• Note the centered dot, normally used when units are multiplied (the kWh is

an exception).

• In addition and subtraction, the answer should have the same number of digits to

the right of the decimal point as the term in the sum or difference that has the

smallest number of digits to the right of the decimal point.

– Example: 3.2492 m – 3.241 = 0.008 m

• Note the loss of accuracy as the answer has only one significant figure.

1.4 Changing units

Clicker question

Choose the sequence that correctly ranks the numbers according to

the number of significant figures. (Rank from fewest to most.)

A. 0.041109 , 3.14 107 , 2.998 10-9 , 0.0008

B. 3.14 107 , 0.041109 , 0.0008, 2.998 10-9

C. 2.998 10-9 , 0.041109 , 0.0008, 3.14 107

D. 0.0008, 0.041109 , 3.14 107 , 2.998 10-9

E. 0.0008, 0.041109 , 2.998 10-9 , 3.14 107

Redefining the meter:

• In 1792 the unit of length, the meter, was defined as one-millionth the

distance from the north pole to the equator.

• Later, the meter was defined as the distance between two finely

engraved lines near the ends of a standard platinum-iridium bar, the

standard meter bar. This bar is placed in the International Bureau of

Weights and Measures near Paris, France.

• In 1960, the meter was defined to be 1 650 763.73 wavelengths of a

particular orange-red light emitted by krypton-86 in a discharge tube that

can be set anywhere in the world.

• In 1983, the meter was defined as the length of the path traveled by light

in a vacuum during the time interval of 1/299 792 458 of a second. The

speed of light is then exactly 299 792 458 m/s.

1.5 Length

1.5 Length

Some examples of lengths

• It’s often sufficient to estimate the answer to a physical calculation, giving the

result to within an order of magnitude or perhaps one significant figure.

• Estimation can provide substantial insight into a problem or physical situation.

• Example: What’s the United States’ yearly gasoline consumption?

• There are about 300 million people in the U.S., so perhaps about 100

million cars (108 cars).

• A typical car goes about 10,000 miles per year (104 miles).

• A typical car gets about 20 miles per gallon.

• So in a year, a typical car uses (104 miles)/(20 miles/gallon) = 500 gal.

• So the United States’ yearly gasoline consumption is about

(500 gal/car)(108 cars) = 51010 gallons.

– That’s about 201010 L or 200 GL.

Slide 1-11

1.5 Length: Estimation

1.5 Length: Estimation

PROBLEM: The world’s largest ball of string is about 2 m in radius.

To the nearest order of magnitude, what is the total length, L, of the

string of the ball?

SETUP: Assume that the ball is a sphere of radius 2 m. In order to

get a simple estimate, assume that the cross section of the string is

a square with a side edge of 4 mm. This overestimate will account

for the loosely packed string with air gaps.

CALCULATE: The total volume of the string is roughly the volume of

the sphere. Therefore,

kmmxmx

mL

RRLxxV

3102)104(

)2(4

43

4)104(

6

23

3

3323

1.6 Time

• Atomic clocks give very

precise time measurements.

• An atomic clock at the

National Institute of

Standards and Technology in

Boulder, CO, is the standard,

and signals are available by

shortwave radio stations.

• In 1967 the standard second

was defined to be the time

taken by:

• 9 192 631 770 oscillations of

the light emitted by cesium-

133 atom.

1.7 Mass

A platinum-iridium cylinder, kept at the

International Bureau of Weights &

Measures near Paris, France, has the

standard mass of 1 kg.

http://en.wikipedia.org/wiki/Kilogram

Another unit of mass is used for atomic

mass measurements. Carbon-12 atom has

a mass of 12 atomic mass units, defined as:

kgxu 271086538660.11

1.7 Density

Density is typically expressed in units

of kg/m3, and is often expressed as

the Greek letter, rho (ρ).

Example, Density and Liquefaction: